Sussex's quarter-final hopes were hanging by a thread going into this week. But after tonight's four-wicket win against high-flying Gloucestershire, a win against the South Group's whipping boys Middlesex tomorrow night will see them through to the knockout stages for the first time since 2015.

Tipped by many as pre-tournament favourites, and boasting a star-studded bowling attack, their season has been blighted by four washouts and a misfiring middle order, and they realistically needed three wins from their last three games to reach the next round.

But two impressive victories in three nights has left them with a simple task: beat Middlesex, and they are through. Gloucestershire's hopes of a home quarter-final are now slim, but Surrey and Glamorgan were the big losers from tonight's game; the pair meet tomorrow night in a must-win for both, but both sides will have to rely on other results to sneak through.

But they will have to cope without their inspirational legspinner Rashid Khan. He will miss the Middlesex match, having been instructed by the Afghanistan Cricket Board to travel to Ireland on Friday ahead of a T20 series which starts on Monday.

Sussex's victory at Bristol saw their attack come to the fore again. Rashid, with three wickets, was predictably the standout, but no bowler went at more than nine-an-over, and stand-in skipper Danny Briggs shuffled his pack brilliantly throughout.

Chasing a gettable 160, they got off to a flying start courtesy of Phil Salt's top-order pyrotechnics.

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One of the few Sussex batsmen whose reputation could be said to have improved over the course of this tournament, Salt peppered the short straight boundaries with a series of powerplay boundaries both down the ground and over fine leg and third man. When he was out for an enterprising 60 at the end of the ninth over, the required rate was just 6.8.

The chase would not prove as straightforward as it might have been. Left-arm wrist-spin has not dominated the English summer in the way some thought it might after Kuldeep Yadav's remarkable start to the white-ball leg of India's tour, but it had a part to play here.

While Kuldeep was taking 6 for 25 in the Trent Bridge ODI, Jake Lintott bowled 18 wicketless overs for Gloucestershire's Seconds in a three-day friendly at Rockhampton. But on first-team debut here, he bamboozled Sussex's top order, removing Laurie Evans and Delray Rawlins with the fifth and sixth balls of his first over to change the complexion of the run chase.

Lintott is something of a journeyman for a man playing only his second professional game: he has had spells playing minor counties cricket, and turned out for a spate of county second teams. At 25, he will hope that showings like this can secure him a run in the first team and help him tie down a contract.

"I only knew I was playing about an hour and a half before the game," he said. "Tom Smith was not available so I got the call to take his place. I'd be lying if I said I wasn't nervous when the skipper tossed me the ball and I just tried to get it to the other end as fast as possible.

"I have played against Delray Rawlins a number of times and he usually hits me all over the park so it was good to bowl only one ball at him tonight."

David Wiese - picked ahead of Tom Bruce, the New Zealand international who has struggled to find any kind of form - came in and struck the ball cleanly from the outset. With Harry Finch holding up an end and rotating the strike, Wiese clubbed Lintott for two boundaries in succession, and when he repeated that trick in the 16th over, it looked like the game was won.

It wasn't; not quite. Looking for a third blow to the rope, Wiese heaved Benny Howell down the ground, but only as far as Jack Taylor at long-on. The batsmen had crossed, before Finch edged behind to Howell's next ball. Again, the run chase looked to have lost impetus.

But Jofra Archer calmed the jangling nerves in the Sussex dressing room with a pair of boundaries, and, even after he had strangled David Payne down the legside, the win was sealed with an over to spare.

In truth, Gloucestershire always looked 15 runs short of a par score. Their 159 for 9 was the lowest total batting first at this ground this season, held together only by Michael Klinger's restrained 59.

After Miles Hammond's initial flourish, no batsman ever looked set, and the boundaries dried up - there were only two between the end of the Powerplay and the start of the 14th over.

Rashid Khan bowled with the unnerving accuracy and skill that it is easy to take for granted, and ended with 3-24 from his set of four. He now has 17 wickets in the tournament, an economy rate of 6.59, and is surely the world's premier T20 spinner; if Sussex do make the quarters, he will be sorely missed while on international duty.

Crucially, none of Gloucestershire's engine room of Howell, Noema-Barnett, Higgins and Taylor got a score of note; their fast-scoring cameos have been a vital part of the side's batting this season, but all struggled to find the ropes. Even Klinger, usually so fluent, failed to find his normal rhythm, and the game was always Sussex's to lose.